[jonbronson]

That's self-evidently untrue. The properties that make a circle would be true regardless of whether a human ever set eyes on a perfect circle. Us identifying those properties is an act of discovery via research. Codifying those mathematical truths into a written notation is the only component of the process that could really be called invention.

[jhedwards]

It's not self-evidently untrue, this is an incredibly complex philosophical question with no easy "right answer". There is also a spectrum of positions about this.

The Stanford Encyclopedia of Philosophy is a good resource for reading about this topic: https://plato.stanford.edu/entries/platonism-mathematics/#Ob...

Edit: another good link: https://plato.stanford.edu/entries/nominalism-mathematics/

[b3kart]

No human has ever set eyes on a perfect circle, because it (most likely) doesn't exist in nature. As such, I would argue that a perfect circle is a concept (or a model, if you will) that we've invented to make it easier for us to deal with an imperfect real world. I would not call identifying properties of such a model an act of discovery: one can come up with any model, no matter how far from reality, and use some set of axioms to identify its properties, but none of it will make said model real or fundamental in any way. The best we can hope for is that the model will be useful for making predictions about the real world.

[UncleMeat]

But we still chose the labels. We chose what the elevate to the level of a mathematical object. Heck, even the idea of "what is true" is not universal in mathematics. Intuitionist and classical logic have different ideas of what. it means.

[moffkalast]

Well it really depends on how far you push the definition. There are inherent properties that can be discovered, but the way they're calculated and described is purely arbitrary. You need to get the same result of an area of a circle in the end, but how you get there is invented. Far more feasible and evident for complex stuff than the basics of course.

As shown in the video, the depressed quadratic was basically solved by 3 people in 3 different ways, with today's description and definition being different from that too.